Understanding spurious regressions in econometrics (Q1082027)

Regression equations which relate two or more time series represented by integrated random processes of the ARIMA type, frequently have \(R^ 2\) yet display highly autocorrelated residuals indicated by very low Durban- Watson statistics. In such situations the usual signficance tests on the regression coefficients are very misleading. The present paper develops an asymptotic theory for such regressions, which explains as a special case the spurious regressions where the usual t-ratio significance test is shown to diverge as the sample size gets infinitely large. This asymptotic theory is also extended to multiple regressions where the variables are generated by a general vector integrated process.